Supervised Learning for User Behavior over Time

Question

I want to use machine learning to identify the signature of a user who converts to a subscriber of a website given their behavior over time.

Let's say my website has 6 different features which can be used before subscribing and users can convert to a subscriber at any time.

For a given user I have stats which represent the intensity on a continuous range of that user's interaction with features 1-6 on a daily basis so:

• D1: f1,f2,f3,f4,f5,f6
• D2: f1,f2,f3,f4,f5,f6
• D3: f1,f2,f3,f4,f5,f6
• D4: f1,f2,f3,f4,f5,f6

Let's say on day 5, the user converts.

What machine using algorithms would help me identify which are the most common patterns in feature usage which lead to a conversion?

(I know this is a super basic classification question, but I couldn't find a good example using longitudinal data, where input vectors are ordered by time like I have)

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To develop the problem further, let's assume that each feature has 3 intensities at which the user can interact (H, M, L).

We can then represent each user as a string of states of interaction intensity. So, for a user:

• LLLLMM LLMMHH LLHHHH

Would mean on day one they only interacted significantly with features 5 and 6, but by the third day they were interacting highly with features 3 through 6.

N-gram Style

I could make these states words and the lifetime of a user a sentence. (Would probably need to add a "conversion" word to the vocabulary as well)

If I ran these "sentences" through an n-gram model, I could get the likely future state of a user given his/her past few state which is somewhat interesting. But, what I really want to know the most common sets of n-grams that lead to the conversion word. Rather than feeding in an n-gram and getting the next predicted word, I want to give the predicted word and get back the 10 most common n-grams (from my data) which would be likely to lead to the word.

Amaç Herdağdelen suggests identifying n-grams to practical n and then counting how many n-gram states each user has. Then correlating with conversion data (I guess no conversion word in this example). My concern is that there would be too many n-grams to make this method practical. (if each state has 729 possibilities, and we're using trigrams, thats a lot of possible trigrams!)

Alternatively, could I just go thru the data logging the n-grams which led to the conversion word and then run some type of clustering on them to see what the common paths are to a conversion?

Survival Style

Suggested by Iterator, I understand the analogy to a survival problem, but the literature here seems to focus on predicting time to death as opposed to the common sequence of events which leads to death. Further, when looking up the Cox Proportional Hazard model, I found that it does not event accommodate variables which change over time (its good for differentiating between static attributes like gender and ethnicity)- so it seems very much geared toward a different question than mine.

Decision Tree Style

This seems promising though I can't completely wrap my mind around how to structure the data. Since the data is not flat, is the tree modeling the chance of moving from one state to another down the line and when it leads to conversion or not? This is very different than the decision tree data literature I've been able to find.

Also, need clarity on how to identify patterns which lead to conversion instead a models predicts likely hood of conversion after a given sequence.

Answer 1

Theoretically, hidden markov models may be a suitable solution to your problem. The features on your site would constitute the alphabet, and you can use the sequence of interactions as positive or negative instances depending on whether a user finally subscribed or not. I don't have a guess about what the number of hidden states should be, but finding a suitable value for that parameter is part of the problem, after all.

As a side note, positive instances are trivial to identify, but the fact that a user has not subscribed so far doesn't necessarily mean s/he won't. You might consider to limit your data to sufficiently old users.

I would also consider converting the data to fixed-length vectors and apply conceptually simpler models that could give you some intuition about what's going on. You could use n-grams (consecutive interaction sequences of length n).

As an example, assuming that the interaction sequence of a given user ise "f1,f3,f5", "f1,f3,f5" would constitute a 3-gram (trigram). Similarly, for the same user and the same interaction sequence you would have "f1,f3" and "f3,f5" as the 2-grams (bigrams). In order to represent each user as a vector, you would identify all n-grams up to a practical n, and count how many times the user employed a given n-gram. Each column in the vector would represent the number of times a given n-gram is observed for a given user.

Then -- probably with the help of some suitable normalization techniques such as pointwise mutual information or tf-idf -- you could look at the correlation between the n-grams and the final outcome to get a sense of what's going on, carry out feature selection to find the most prominent sequences that users are involved in, or apply classification methods such as nearest neighbor, support machine or naive Bayes to build a predictive model.